Prove that the set {fr1,…,frk}{\displaystyle \{f_{r_{1}},\dots ,f_{r_{k}}\}} is linearly independent.

Problem 6

(This refers to the value T(64)=18,446,744,073,709,551,615{\displaystyle T(64)=18,446,744,073,709,551,615} given in the computer code below.) Transferring one disk per second, how many years would it take the priests at the Tower of Hanoi to finish the job?